The lecture will be in English (BMS course).
| Lecturer: |
Robert Altmann |
|
| Lectures: |
Tue 12-14 in MA 551 |
|
Wed 10-12 in MA 549 |
Exams:
There will be oral exams (~ 35 min) at the end of the semester.
- Thursday, September 7 (room MA 461)
- Monday, September 18 (room MA 461)
- mathematical fundamentals in system and control theory
- analysis of control systems: controllability, stabilizability, observability, reconstructability, detectability
- Lyapunov equations and stability theory
- optimal control problems
- algebraic Riccati equations
There will be six exercise sheets (roughly every two weeks). Some parts will be distributed as written exercises, solutions will be discussed - mainly by the students - within the lectures.
- 18.04: introduction, repetition (ODEs)
- 19.04: repetition (Laplace transform, SVD, invariant subspaces), inverted pendulum
- 25.04: control systems in frequency domain
- 26.04: discussion of 1. Exercise
- 02.05: controllability Gramian
- 03.05: controllability matrix, Kalman decomposition
- 09.05: Hautus-Popov lemma, stabilizability
- 10.05: discussion of 2. Exercise
- 16.05: reconstructability, observability
- 17.05: detectability, feedback equivalence
- 23.05: discussion of 3. Exercise
- 24.05: staircase form
- 30.05: Sylvester equation
- 31.05: Lyapunov equation
- 06.06: numerical solution of Lyapunov equations (Kronecker)
- 07.06: Bartels-Stewart
- 13.06: discussion of 4. Exercise
- 14.06: matrix sign function method, partial stabilization
- 20.06: pole placement I
- 21.06: pole placement II
- 27.06: --- no lecture ---
- 28.06: discussion of 5. Exercise
- 04.07: pole placement algorithms
- 05.07: optimal control with differential Riccati equation
- 11.07: algebraic Riccati equation
- 12.07: discussion of 6. Exercise
- 18.07: algorithm of Laub for solving the ARE
- 19.07: Newton method for solving the ARE